A hybrid optimization-simulation approach for robust weekly aircraft routing and retiming

We address the robust weekly aircraft routing and retiming problem, which requires determining weekly schedules for a heterogeneous fleet that maximizes the aircraft on-time performance, minimizes the total delay, and minimizes the number of delayed passengers. The fleet is required to serve a set of flights having known departure time windows while satisfying maintenance constraints. All flights are subject to random delays that may propagate through the network. We propose to solve this problem using a hybrid optimization-simulation approach based on a novel mixed-integer nonlinear programming model for the robust weekly aircraft maintenance routing problem. For this model, we provide an equivalent mixed-integer linear programming formulation that can be solved using a commercial solver. Furthermore, we describe a Monte-Carlo-based procedure for sequentially adjusting the flight departure times. We perform an extensive computational study using instances obtained from a major international airline, having up to 3387 flights and 164 aircraft, which demonstrates the efficacy of the proposed approach. Using the simulation software SimAir to assess the robustness of the solutions produced by our approach in comparison with that for the original solutions implemented by the airline, we found that on-time performance was improved by 9.8–16.0%, cumulative delay was reduced by 25.4–33.1%, and the number of delayed passengers was reduced by 8.2–51.6%.     

Dynamic yield management when aircraft assignments are subject to swap

As a practical form of demand driven dispatch at some major airlines in North America, cockpit compatible aircraft of different capacities are paired in the fleet assignment for a possible future swap on the two involved flights. They are paired in such a way that the swap does not affect their aircraft routings on other legs. The swap decision depends on demand realization on the two flights and is made at a predetermined time prior to departure. Yield management on the two flights is studied in this paper. We begin by studying a base problem in which at a certain time before departure, the assignment on a flight is subject to change with a fixed probability. The base problem extends the threshold policy into the case where future capacity is uncertain. Secondly, we propose a heuristic for yield management over two flights with swappable aircraft by repeatedly updating the swap probability as demand unfolds. Our numerical result shows that this policy significantly enhances the airline’s capability to increase revenue under demand driven dispatch. In addition, the base problem may shed lights on derivation of optimal yield management policy in irregular operational settings where final capacity assignment is independent of yield management policy.     

An optimization model for aircraft maintenance scheduling and re-assignment

The aircraft maintenance scheduling is one among the major decisions an airline has to make during its operation. Though maintenance scheduling comes as an end stage in an airline operation, it has potential for cost savings. Maintenance scheduling is an easily understood but difficult to solve problem. Given a flight schedule with aircraft assigned to it, the aircraft maintenance-scheduling problem is to determine which aircraft should fly which segment and when and where each aircraft should undergo different levels of maintenance check required by the Federal Aviation Administration. The objective is to minimize the maintenance cost and any costs incurred during the re-assignment of aircraft to the flight segments.This paper provides a complete formulation for maintenance scheduling and a heuristic approach to solve the problem. The heuristic procedure provides good solutions in reasonable computation time. This model can be used by mid-sized airline corporations to optimize their maintenance costs.     

A multiobjective model for maximizing fleet availability under the presence of flight and maintenance requirements

Every aircraft, military or civilian, must be grounded for maintenance after it has completed a certain number of flight hours since its last maintenance check. In this paper, we address the problem of deciding which available aircraft should fly and for how long, and which grounded aircraft should perform maintenance operations, in a group of aircraft that comprise a combat unit. The objective is to achieve maximum availability of the unit over the planning horizon. We develop a multiobjective optimization model for this problem, and we illustrate its application and solution on a real life instance drawn from the Hellenic Air Force. We also propose two heuristic approaches for solving large scale instances of the problem. We conclude with a discussion that gives insight into the behavior of the model and of the heuristics, based on the analysis of the results obtained.     

Network models for seat allocation on flights

This paper examines the problem of proper (optimal) control over the seat allocation on flights. Given a heterogeneous fleet of aircraft types, multi-leg flights, a number of different passenger categories, and cancelations, an airline's objective is to devise an effective system which aids in setting the seat allocation targets for each category of passengers on each flight. This issue is analyzed by a number of authors in the context of economic, simulation based, probabilistic, and mathematical programming studies. We present an attempt to address this problem from the systems prospective emphasizing characteristics such as: passenger cancelations, multi-leg flights, and rolling tactical planning time horizon. Starting from a very simple network flow models for a single flight with a number of intermediate stops, a number of progressively complex models are presented. The airline flights and the seat allocation system are represented as a generalized network flow model (with gains/losses on arcs) with the objective of flow maximization (profit maximization). This modelling approach does not claim to replace the seat allocation approaches presented in Alstrup et al. (1985), Mayer (1976), Richter (1982), Simpson (1985a), and Wang (1983), but rather construct seat allocations utilizing some of those referenced schemes in a parameter setting mode for a large network model. The objective of this paper is not to report on computational experiments, but to present a modeling approach which seems to be promising, if somewhat speculative.     

Prediction of aircraft performances based on data collected by air traffic control centers

Accurate prediction of aircraft position is becoming more and more important for the future of air traffic. Currently, the lack of information about flights prevents us to fulfill future demands for the needed accuracy in 4D trajectory prediction. Until we get the necessary information from aircraft and until new more accurate methods are implemented and used, we propose an alternative method for predicting aircraft performances using machine learning from historical data about past flights collected in a multidimensional database. In that way, we can improve existing applications by providing them better inputs for their trajectory calculations. Our method uses flight plan data to predict performance values, which are suited individually for each flight. The results show that based on recorded past aircraft performances and related flight data we can effectively predict performances for future flights based on how similar flights behaved in the past.     

Robust weekly aircraft maintenance routing problem and the extension to the tail assignment problem

In this paper, we study two closely related airline planning problems: the robust weekly aircraft maintenance routing problem (RWAMRP) and the tail assignment problem (TAP). In real life operations, the RWAMRP solution is used in tactical planning whereas the TAP solution is implemented in operational planning. The main objective of these two problems is to minimize the total expected propagated delay (EPD) of the aircraft routes. To formulate the RWAMRP, we propose a novel weekly line-of-flights (LOF) network model that can handle complex and nonlinear cost functions of EPD. Because the number of LOFs grows exponentially with the number of flights to be scheduled, we propose a two-stage column generation approach to efficiently solve large-scale real-life RWAMRPs. Because the EPD of an LOF is highly nonlinear and can be very time-consuming to accurately compute, we propose three lower bounds on the EPD to solve the pricing subproblem of the column generation. Our approach is tested on eight real-life test instances. The computational results show that the proposed approach provides very tight LP relaxation (within 0.6% of optimal solutions) and solves the test case with more than 6000 flights per week in less than three hours. We also investigate the solutions obtained by our approach over 500 simulated realizations. The simulation results demonstrate that, in all eight test instances, our solutions result in less EPDs than those obtained from traditional methods. We then extend our model and solution approach to solve realistically simulated TAP instances.     

The planning of aircraft routes and flight frequencies in an airline network operations

This research is aimed at developing a model that maximizes system profit when determining the aircraft routes and flight frequencies in a network. The model employs network flow techniques to effectively collect or deliver passenger flows from all origins to all destinations using non‐stop and multi‐stop flights in multi‐fleet operations. The model was formulated as a multi‐commodity network flow problem. A Lagrangian‐based algorithm was developed to solve the problem. To test the model in practice, a case study is presented.     

Heuristic approach to the airline schedule disturbances problem

Abstract

When disturbances make it impossible to realise the planned flight schedule, the dispatcher at the airline operational centre defines a new flight schedule based on airline policy, in order to reduce the negative effects of these perturbations. Depending on airline policy, when designing the new flight schedule, the dispatcher delays or cancels some flights and reassigns some flights to available aircraft. In this paper, a decision support system (DSS) for solving the airline schedule disturbances problem is developed aiming to assist decision makers in handling disturbances in real-time. The system is based on a heuristic algorithm, which generates a list of different feasible schedules ordered according to the value of an objective function. The dispatcher can thus select and implement one of them. In this paper, the possibilities of DSS are illustrated by real numerical examples that concern JAT Airways' flight schedule disturbances.     

Short-term planning of liquefied natural gas deliveries

The ability of a supplier of liquefied natural gas (LNG) to deliver cargoes at desired times, while effectively managing a fleet of cryogenic vessels can significantly impact its profits. We investigate in this paper an LNG short-term delivery planning problem by considering mandatory cargoes as well as optional cargoes to select, along with the scheduling of a heterogeneous vessel fleet with controllable cruising speeds. Several technical constraints are accommodated including time windows, berth availability, bunkering restrictions, inventory, liquefaction terminal storage capacity, maximum waiting time, and planned maintenance restrictions. The objective is to maximize the net profit.We propose a mixed-integer programming formulation that includes a polynomial number of variables and constraints and accommodates all of the problem features. Also, we describe an optimization-based variable neighborhood search procedure that embeds the proposed compact formulation. To assess the quality of the generated solutions, we propose a second valid formulation with an exponential number of decision variables and we solve its linear programming relaxation using column generation. We provide the results of extensive computational results that were carried out on a set of large-scale set of realistic instances, with up to 62 vessels and 160 cargoes, provided by a major LNG producer. These results provide evidence that the proposed improvement procedure yields high-quality solutions.     

A heuristic model for frequency planning and aircraft routing in small size airlines

The flight schedule of an airline is the primary factor in finding the most effective and efficient deployment of the airline's resources. The flight schedule process aims at finding a set of routes with associated aircraft type, frequency of service and times of departures and arrivals in order to satisfy a specific objective such as profit maximization. In this paper, we develop a two‐phase heuristic model for airline frequency planning and aircraft routing for small size airlines. The first phase develops a frequency plan using an economic equilibrium model between passenger demand for flying a particular route and aircraft operating characteristics. The second phase uses a time‐of‐day model to develop an assignment algorithm for aircraft routing.     

Future electricity demand from battery‐powered vehicles

An important decision faced by airline schedulers is how to adapt the flight schedule and aircraft assignment to unforeseen perturbations in an established schedule. In the face of unforeseen aircraft delays, schedulers have to decide which flights to delay, and when delays become excessive, which to cancel. Current scheduling models deal with simple decision problems of delay or cancellation, but not with both simultaneously. But in practice the optimal decision may involve results from the integration of both flight cancellations and delays. In Part I of this paper, a quadratic programming model for the integration decision problem is given. The model can formulate the integration of flight cancellations and delays as well as some special cases, such as the ferrying of surplus aircraft and the possibility of swapping different types of aircraft. In this paper, based on the special structure of the model, an effective algorithm is presented, sufficient computational experiments are conducted and some results are reported. These show that we can expect to obtain a sufficiently good solution in terms of reasonable CPU time.     

An optimal aircraft fleet management decision model under uncertainty

Decision planning for an efficient fleet management is crucial for airlines to ensure a profit while maintaining a good level of service. Fleet management involves acquisition and leasing of aircraft to meet travelers' demand. Accordingly, the methods used in modeling travelers' demand are crucial as they could affect the robustness and accuracy of the solutions. Compared with most of the existing studies that consider deterministic demand, this study proposes a new methodology to find optimal solutions for a fleet management decision model by considering stochastic demand. The proposed methodology comes in threefold. First, a five‐step modeling framework, which is incorporated with a stochastic demand index (SDI), is proposed to capture the occurrence of uncertain events that could affect the travelers' demand. Second, a probabilistic dynamic programming model is developed to optimize the fleet management model. Third, a probable phenomenon indicator is defined to capture the targeted level of service that could be achieved satisfactorily by the airlines under uncertainty. An illustrative case study is presented to evaluate the applicability of the proposed methodology. The results show that it is viable to provide optimal solutions for the aircraft fleet management model. Copyright © 2013 John Wiley & Sons, Ltd.     

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.     

What are the implications of climate change for trans-Atlantic aircraft routing and flight time?

The effect of wind changes on aircraft routing has been identified as a potential impact of climate change on aviation. This is of particular interest for trans-Atlantic flights, where the pattern of upper-level winds over the north Atlantic, in particular the location and strength of the jet stream, strongly influences both the optimal flight route and the resulting flight time. Eastbound trans-Atlantic flights can often be routed to take advantage of the strong tailwinds in the jet stream, shortening the flight time and reducing fuel consumption. Here we investigate the impact of climate change on upper-level winds over the north Atlantic, using five climate model simulations from the Fifth Coupled Model Intercomparison Project, considering a high greenhouse-gas emissions scenario. The impact on aircraft routing and flight time are quantified using flight routing software. The climate models agree that the jet stream will be on average located 1° further north, with a small increase in mean strength, by 2100. However daily variations in both its location and speed are significantly larger than the magnitude of any changes due to climate change. The net effect of climate change on trans-Atlantic aircraft routes is small; in the annual-mean eastbound routes are 1 min shorter and located further north and westbound routes are 1 min longer and more spread out around the great circle. There are, however, seasonal variations; route time changes are larger in winter, while in summer both eastbound and westbound route times increase.     

Anomaly detection via a Gaussian Mixture Model for flight operation and safety monitoring

Safety is key to civil aviation. To further improve its already respectable safety records, the airline industry is transitioning towards a proactive approach which anticipates and mitigates risks before incidents occur. This approach requires continuous monitoring and analysis of flight operations; however, modern aircraft systems have become increasingly complex to a degree that traditional analytical methods have reached their limits – the current methods in use can only detect ‘hazardous’ behaviors on a pre-defined list; they will miss important risks that are unlisted or unknown. This paper presents a novel approach to apply data mining in flight data analysis allowing airline safety experts to identify latent risks from daily operations without specifying what to look for in advance. In this approach, we apply a Gaussian Mixture Model (GMM) based clustering to digital flight data in order to detect flights with unusual data patterns. These flights may indicate an increased level of risks under the assumption that normal flights share common patterns, while anomalies do not. Safety experts can then review these flights in detail to identify risks, if any. Compared with other data-driven methods to monitor flight operations, this approach, referred to as ClusterAD-DataSample, can (1) better establish the norm by automatically recognizing multiple typical patterns of flight operations, and (2) pinpoint which part of a detected flight is abnormal. Evaluation of ClusterAD-DataSample was performed on two sets of A320 flight data of real-world airline operations; results showed that ClusterAD-DataSample was able to detect abnormal flights with elevated risks, which make it a promising tool for airline operators to identify early signs of safety degradation even if the criteria are unknown a priori.     

Robust flight-to-gate assignment using flight presence probabilities

In this paper we present a novel method to improve the robustness of solutions to the Flight-to-Gate Assignment Problem (FGAP), with the aim to reduce the need for gate re-planning due to unpredicted flight schedule disturbances in the daily operations at an airport. We propose an approach in which the deterministic gate constraints are replaced by stochastic gate constraints that incorporate the inherent stochastic flight delays in such a way so as to ensure that the expected gate conflict probability of two flights assigned to the same gate at the same time does not exceed a user-specified value. The novel approach is integrated into an existing multiple time slot FGAP model that relies on a binary integer programming formulation and is tested using real-life data pertaining to Amsterdam Airport Schiphol. The results confirm that the proposed approach holds out great promise to improve the robustness of the FGAP solutions.     

A hybrid heuristic strategy for liquefied natural gas inventory routing

As liquefied natural gas (LNG) steadily grows to be a common mode for commercializing natural gas, LNG supply chain optimization is becoming a key technology for gas companies to maintain competitiveness. This paper develops methods for improving the solutions for a previously stated form of an LNG inventory routing problem (LNG-IRP). Motivated by the poor performance of a Dantzig-Wolfe-based decomposition approach for exact solutions, we develop a suite of advanced heuristic techniques and propose a hybrid heuristic strategy aiming to achieve improved solutions in shorter computational time. The heuristics include two phases: the advanced construction phase is based on a rolling time algorithm and a greedy randomized adaptive search procedure (GRASP); and the solution improvement phase is a series of novel MIP-based neighborhood search techniques. The proposed algorithms are evaluated based on a set of realistic large-scale instances seen in recent literature. Extensive computational results indicate that the hybrid heuristic strategy is able to obtain optimal or near optimal feasible solutions substantially faster than commercial optimization software and also the previously proposed heuristic methods.     

An optimization model for a real-time flight scheduling problem

Although airlines plan aircraft routes and crew schedules in advance, perturbations occur everyday. As a result, flight schedules may become infeasible and would need to be updated. This Day of Operations Scheduling problem impacts the entire system of an airline as the decisions enforced are final. When perturbations are relatively small, the airline may be able to at least preserve the planned aircraft and crew itineraries. We propose a model that determines new flight schedules based on planned crew transfers, rest periods, passenger connections, and maintenance. Its dual is shown to be a network model, hence solvable in a real-time environment. In addition, it can be used in more sophisticated operational and planning systems.     

Disruption Management of an Inequality-Based Multi-Fleet Airline Schedule by a Multi-Objective Genetic Algorithm

Abstract

This paper presents a novel application of a Method of Inequality-based Multi-objective Genetic Algorithm (MMGA) to generate an efficient time-effective multi-fleet aircraft routing algorithm in response to the schedule disruption of short-haul flights. It attempts to optimize objective functions involving ground turn-around times, flight connections, flight swaps, total flight delay time and a 30-minute maximum delay time of original schedules. The MMGA approach, which combines a traditional Genetic Algorithm (GA) with a multi-objective optimization method, can address multiple objectives at the same time, then explore the optimal solution. The airline schedule disruption management problem is traditionally solved by Operations Research (OR) techniques that always require a precise mathematical model. However, airline operations involve too many factors that must be considered dynamically, making a precise mathematical model difficult to define. Experimental results based on a real airline flight schedule demonstrate that the proposed method, Multi-objective Optimization Airline Disruption Management by GA, can recover the perturbation efficiently within a very short time. Our results further demonstrate that the application can yield high quality solutions quickly and, consequently, has potential to be employed as a real-time decision support tool for practical complex airline operations.